Linear Codes

Abstract

In this chapter we assume that information is coded using an alphabet Q with q distinct symbols. A code is called a block code if the coded information can be divided into blocks of n symbols which can be decoded independently. These blocks are the codewords and n is called the block length or word length (or just length). The examples in Chapter 2 were all block codes. In Chapter 13 we shall briefly discuss a completely different system, called convolutional coding, where an infinite sequence of information symbols i ₀, i ₁, i₂,… is coded into an infinite sequence of message symbols. For example, for rate $\frac{1}{2}$ one could have i ₀, i ₁, i ₂,… → i ₀, i’ ₀, i ₁, i’ ₁,…, where i’ _n is a function of i ₀, i ₁,…, i _n . For block codes we generalize (2.1.3) to arbitrary alphabets.